So far, you've learned about estimating sums and estimating differences.
In this lesson, we're going to explore how to estimate products.
Remember, a product is the answer we get when multiplying.
Estimating a product is done by first rounding the factors to the nearest ten or hundred, then finding a product that is close to the exact answer.
Let's try estimating products together.
One way to estimate products is to round the factors to the closest multiple of 10.
First, let's review:
When multiplying by multiples of 10, multiply the non-zero parts first. Then add back the zeros to the right of the product.
For example:
Estimate 4 × 27
First, let's round the larger factor. What is the closest multiple of 10 to 27?
27 is closest to 30.
Let's rewrite our equation:
4 × 30 = ?
That's pretty easy to solve. We don't need to round the other factor.
Let's multiply the non-zero parts first.
4 × 3 = 12
Next, add back the zero to the right of the product.
120
So, the estimated product of 4 × 27 is 120.
We can also write it with the approximate symbol which looks like this ≈.
4 × 27 ≈ 120
Estimate 47 × 82.
This time, let's round both factors, since the math is a little harder.
47 rounded to the nearest ten is 50.
82 rounded to the nearest ten is 80.
That's a much easier multiplication problem.
50 × 80 = ?
We multiply the non-zero digits first.
5 × 8 = 40
Then we add two zeros at the end. These are the zeros from our factors.
4000
So the estimate for 47 × 82 is 4,000.
We can write our answer this way:
47 × 82 ≈ 4,000
Tip: We did not use an equal sign because what we have is an estimate. We used the "approximate" symbol instead (≈).
"Approximate" means "almost equal to".
Estimate 419 × 61.
The first step is to round the numbers to the highest place value.
What's 419 rounded to the nearest hundred?
That's right, it's 400.
61 rounded to the nearest ten is 60.
Now let's multiply the rounded numbers.
400 × 60 = ?
Let's use our trick for multiplying numbers ending in zeros.
First, we multiply the non-zero digits.
4 × 6 = 24
Now, we add back the zeros from the rounded numbers.
There are 2 zeros in 400, and 1 zero in 60. That's a total of 3 zeros.
24,000
This means 419 × 61 is about 24,000.
Let's learn another way to estimate products.
Estimate 24 × 395.
Let's turn these into compatible numbers.
A compatible number is a number that is familiar to you because you use it in everyday life.
25 is a compatible number because you can think of it as quarters.
Numbers ending in zeros are also compatible numbers.
25 is a compatible number to 24.
400 is a compatible number to 395.
Let's multiply these compatible numbers.
25 × 400 = ?
We multiply the non-zero numbers first.
25 × 4 = ?
Think of this as 4 quarters. 🧐
4 quarters is 100 cents. So 25 x 4 is 100.
25 × 4 = 100
Let's add the two zeros from 400 at the end.
10000
This means 24 × 395 is about 10,000.
24 × 395 ≈ 10,000
Great job.
Now, try the practice to master what you've learned.